Finite Group DatabasebetaFinite Group Databasebeta| order | 26964 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×Dic107 |
| unambiguous semidirect product | C107⋊(C3×C4×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic107)⋊C32 |
| unambiguous semidirect product | (C3×C7×Dic107)⋊C3 |
| derived, Hall | C7×C107 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C107 ⋊ C4 |
| Hall | C7×Dic107 ⋊ C32 |
| Sylow | C107 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×Dic107 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8988 |
1650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26964, 38);